Nonlocal Thermoelasticity Research Articles

Effect of Internal Heat Source on a Nonlocal Thermoelastic Rotating Medium in the Context of a Dual-Phase-Lag Model with Fractional Derivative

Effect of Internal Heat Source on a Nonlocal Thermoelastic Rotating Medium in the Context of a Dual-Phase-Lag Model with Fractional Derivative

Analysis of reflection of wave propagation in magneto-thermoelastic nonlocal micropolar orthotropic medium at impedance boundary

PurposeThis study aims to examine the plane wave reflection problem in micropolar orthotropic magneto-thermoelastic half space, considering the influence of impedance as a boundary in a nonlocal elasticity.Design/methodology/approachThis study presents the novel formulation of governing partial differential equations for micropolar orthotropic medium with impact of nonlocal thermo-elasticity under magnetic field.FindingsThis study provides the numerical results validation for a particular numerical data and expression for the amplitude ratios of reflected waves and identifies the existence of four different waves, namely, quasi longitudinal displacement qCLD-wave, quasi thermal wave qCT-wave, quasi transverse displacement qCTD-wave and quasi-transverse micro-rotational qCTM-wave. The study derives the velocity equation giving the speed and phase velocity of these waves. The study also shows that the small-scale size effect gives significant impact on phase velocity.Research limitations/implicationsThe graphical analysis examines the variation of speeds and coefficients of attenuation of these waves due to frequency, magnetic field and nonlocal parameters. Also, significant conclusions on the variation of reflection coefficient against nonlocal parameter, frequency, impedance parameter and angle of incidence are provided graphically.Practical implicationsThe creation of more effective micropolar orthotropic anisotropic materials which are very useful in the daily life and their applications in earth science are greatly impacted by the findings of this study.Originality/valueThe authors of the submitted document initiated and produced it collectively, with equal contributions from all members.

Mechanical-Acoustic Waves with Two Temperature Nonlocal Thermoelasticity Theory Subjected to Decaying Heat Source

Mechanical-Acoustic Waves with Two Temperature Nonlocal Thermoelasticity Theory Subjected to Decaying Heat Source

Fractional Boundary Element Solution for Nonlinear Nonlocal Thermoelastic Problems of Anisotropic Fibrous Polymer Nanomaterials

This paper provides a new fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems with anisotropic fibrous polymer nanoparticles. This comprehensive BEM solution comprises two solutions: the anisotropic fibrous polymer nanoparticles problem solution and the nonlinear nonlocal thermoelasticity problem. The nonlinear nonlocal thermoelasticity problem solution separates the displacement field into complimentary and specific components. The overall displacement is obtained using the boundary element methodology, which solves a Navier-type problem, and the specific displacement is derived using the local radial point interpolation method (LRPIM). The new modified shift-splitting (NMSS) technique, which minimizes memory and processing time requirements, was utilized to solve BEM-created linear systems. The performance of NMSS was evaluated. The numerical results show how fractional and graded parameters influence the thermal stresses of nonlinear nonlocal thermoelastic issues involving anisotropic fibrous polymer nanoparticles. The numerical findings further reveal that the BEM results correlate very well with the finite element method (FEM) and analytical results, demonstrating the validity and correctness of the proposed methodology.

A Two-Temperature Nonlocal Poro-Thermoelastic Solid Via Higher-Order Time-Derivatives Model with Phase Lag

Abstract Purpose The present study has depicted the effect of gravitational on a two-temperature nonlocal poro-thermoelastic solid. Methods The multi-phase-lag model and fractional derivatives are used to tackle the issue. Through normal mode analysis, analytical formulas for the variable fields are derived. Using appropriate boundary conditions, the physical fields are calculated and the numerical computations have been carried out with the help of MATLAB programming. Results Through a careful comparison of the numerical data, the impacts of gravity, fractional derivative order, and locatiy on the behavior of physical fields are described. Conclusion Physical variables are affected by nonlocal thermoelasticity, fractional derivative order as well as the gravity field.

Thermoelastic diffusion in nonlocal orthotropic medium with porosity

The present article investigates the linear theory of nonlocal thermoelasticity in homogeneous orthotropic porous medium with diffusion in the context of dual-phase-lag model. The focal point of the present study involves an examination of Fick’s mass diffusion law and the generalized Fourier’s law within the context of the dual-phase-lag model of hyperbolic thermoelasticity. The incorporation of voids, mass diffusion with phase lagging in the diffusion flux is the basis for establishing the void diffusion-elasticity models. Furthermore, the new dual-phase-lag diffusion model introduces the consideration of nonlocal effects in mass transfer. The resolution of the problem involves the utilization of normal mode analysis, employed for solving, and encompasses the application of thermal shock at the surface boundary. Numerical calculations of stress components, displacement components, voids, temperature, and concentration of the diffusive material are performed for various distances and time intervals.

Effect of non-local thermoelasticity on diffusion under hydrostatic pressure

AbstractIn this paper, thermoelastic diffusion theory is demonstrated on a two-dimensional half-space problem. The surface is subjected to thermal shock and hydrostatic loads. The chemical potential must be a known function of time. The solution is obtained by the direct method using the Laplace technique and the Fourier exponential transform. Local and non-local thermoelasticity are discussed, and the influence of non-local parameters on the general theory of thermoelastic diffusion is investigated. Chemical potential, concentration, temperature, stress and displacement distributions are calculated numerically and displayed graphically.

Gravitational Influence on a Nonlocal Thermoelastic Solid with a Heat Source via L–S Theory

PurposeThe purpose is to obtain precise expressions of physical fields using the appropriate non-dimensional variables and normal mode analysis.MethodsBased on the Lord–Shulman (L-S) theory and taking into account gravitational influences as well as temperature-dependent features, the fundamental equations for a nonlocal thermoelastic solid are developed.ResultsWhen a nonlocal thermoelastic media is swapped out for a thermoelastic one, this approach still holds true. Comparisons are done between the outcomes obtained and those expected for various nonlocal parameter values and for an empirical material constant. Additionally, comparisons are done between the outcomes for various gravity field values.ConclusionThe nonlocal parameter plays a big part in how the physical fields are distributed. The distributions of the physical fields are significantly influenced by the gravity field.

2D Problem of a Nonlocal Thermoelastic Diffusion Solid with Gravity via Three Theories

PurposeThe impact of gravity on nonlocal thermoelastic diffusion solid is discussed in this work.Methods The Green-Naghdi theory (G-N II), the Lord-Shulman theory, and the three-phase-lag model all explore the issue. The governing equations are solved using the normal mode technique to get the analytic forms of the displacements, temperatures, force stress tensors, and mass concentration. Using appropriate boundary conditions, the physical fields are calculated and the numerical computations have been carried out with the help of MATLAB programming.Results In the physical domain, numerical results for the field quantities are provided and graphically displayed in both the absence and presence of gravity and the nonlocal parameter.ConclusionPhysical variables are affected by nonlocal thermoelasticity as well as the gravity field.

A Nonlinear Nonlocal Thermoelasticity Euler-Bernoulli Beam Theory and Its Application to Single-Walled Carbon Nanotubes.

Although small-scale effect or thermal stress significantly impact the mechanical properties of nanobeams, their combined effects and the temperature dependence of the elastic parameters have yet to attract the attention of researchers. In the present paper, we propose a new nonlocal nonlinear Euler-Bernoulli theory to model the mechanical properties of nanobeams. We considered the small-scale effect, thermal stress, and the temperature dependence of Young's modulus. A single-walled carbon nanotube (SWCNT) was used to demonstrate the influence of the three factors on elastic buckling and forced bending vibrations. The results indicate that thermal stress and the temperature dependence of Young's modulus have a remarkable influence on the mechanical properties of slender SWCNTs as compared to the small-scale effect induced by the nonlocal effect. Ignoring the temperature effect of slender SWCNTs may cause qualitative mistakes.

Study on reflected waves through visco-elastic solid rotating with fixed angular frequency

The work is about the characteristics study of reflected waves through viscoelastic solid. The solid used has a nanostructure and is semiconductor in nature, with uniform angular frequency. The concept of nonlocal thermoelasticity is considered to study the disturbances propagating through the medium. The refined theory of the multiphase lag heat conduction model is used to encounter the heat disturbance that travels through the medium. We have also considered the concept of fractional order time derivative while analyzing the heat conduction model. Expressions for dispersion relation for the reflected medium are obtained. It is found that four coupled waves reflected into the medium and each wave is neither purely transverse nor dilatational. The analytical results obtained are computed graphically for a particular medium. Characteristics like velocity, attenuation coefficient, and specific heat loss are computed and represented graphically for the medium. In addition to semiconductor nanostructure devices, the findings might be useful in visco-elastic semiconductor nanostructures involved in geology and seismology studies.

State space approach to study thermal shock problem in nonlocal thermoelastic medium with double porosity

In this article, a two-dimensional problem is studied in a homogeneous isotropic thermoelastic medium with double porosity in the context of nonlocal thermoelasticity and the problem is treated in the presence of the Green–Naghdi model of type-III. Constitutive relations and field equations are derived and the state space approach is employed to solve this problem. Thermal shock is applied on the boundary of the surface. From these relations and expressions, we have calculated stress components, displacement components, and temperature for different values of distance and time numerically and plotted graphically to demonstrate and compare theoretical results. The influences of void parameters, locality, and nonlocality on the various physical quantities are also analyzed. Some particular and special cases are also deduced from this study and compared with the existing results.

Generalized Thermoelastic Interactions in an Infinite Viscothermoelastic Medium under the Nonlocal Thermoelastic Model

The wave propagation in viscothermoelastic materials is discussed in the present work using the nonlocal thermoelasticity model. This model was created using the Lord and Shulman generalized thermoelastic model due to the consequences of delay times in the formulations of heat conduction and the motion equations. This model was created using Eringen’s theory of the nonlocal continuum. The linear Kelvin–Voigt viscoelasticity model explains the viscoelastic properties of isotropic material. The analytical solutions for the displacement, temperature, and thermal stress distributions are obtained by the eigenvalues approach with the integral transforms in the Laplace transform techniques. The field functions, namely displacement, temperature, and stress, have been graphically depicted for local and nonlocal viscothermoelastic materials to assess the quality of wave propagation in various outcomes of interest. The results are displayed graphically to illustrate the effects of nonlocal thermoelasticity and viscoelasticity. Comparisons are made with and without thermal relaxation time. The outcomes show that Eringen’s nonlocal viscothemoelasticity theory is a promising criterion for analyzing nanostructures, considering the small size effects.

The Effect of a Nonlocal Thermoelastic Model on a Thermoelastic Material under Fractional Time Derivatives

This article develops a novel nonlocal theory of generalized thermoelastic material based on fractional time derivatives and Eringen’s nonlocal thermoelasticity. An ultra-short pulse laser heats the surface of the medium’s surrounding plane. Using the Laplace transform method, the basic equations and their accompanying boundary conditions were numerically solved. The distribution of thermal stress, temperature and displacement are physical variables for which the eigenvalues approach was employed to generate the analytical solution. Visual representations were used to examine the influence of the nonlocal parameters and fractional time derivative parameters on the wave propagation distributions of the physical fields for materials. The consideration of the nonlocal thermoelasticity theory (nonlocal elasticity and heat conduction) with fractional time derivatives may lead us to conclude that the variations in physical quantities are considerably impacted.

Generalized Thermoelastic Interaction in a Half-Space under a Nonlocal Thermoelastic Model

In the current article, the nonlocal thermoelastic theory is used to discuss the wave propagation in unbounded thermoelastic materials. Due to the inclusion of relaxation time in thermal conduction formulation and the equations of motion, this model was developed using Lord and Shulman’s generalized thermoelastic model. The theory of the nonlocal continuum proposed by Eringen is used to obtain this model. The integral transforms of the Laplace transform methods used to generate an analytical solution for physical variables are utilized to produce the analytical solutions for the thermal stress, displacement, and temperature distribution. The effects of nonlocal parameters and relaxation time on the wave propagation distributions of physical fields for material are visually shown and explored.

Fractal nonlocal thermoelasticity of thin elastic nanobeam with apparent negative thermal conductivity

This study treats a new model of nonlocal fractal thermoelasticity beam theory for nanomaterials characterized by an apparent negative thermal conductivity which occurs in shaped graded materials. The model is based on the new concept of "product-like fractal measure" introduced by Li and Ostoja-Starzewski in their formulation of fractal continuum media with fractal dimension The basic setups of the theory are formulated, yet, we have restricted our analysis for the static case. The effects of fractal dimension on field variables, in particular the lateral deflection and the temperature increment of the resonator were analyzed analytically and graphically. It was observed that the physics of the thin elastic nanobeam is affected by the numerical value of the fractal dimension and the characteristic lengths of the theory. Comparable scenarios observed in complex material structures are obtained and discussed.

Effects of the Nonlocal Thermoelastic Model in a Thermoelastic Nanoscale Material

In this work, a novel nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach. The basic equations are applied under the Green and Naghdi model without energy dissipations. To obtain this model, the theory of the non-local continuum suggested by Eringen is applied. The Laplace transformation technique is used for the basic formulations to obtain the analytical solutions of the thermal stress, the displacement, and the temperature during the nanoscale thermo-electric medium. The inverse of the Laplace transformation is used with the numerical technique to obtain the complete solutions of the studying fields in the time–space domains. The main physical fields are displayed graphically and theoretically discussed under the influence of nonlocal parameters.

TEMPERATURE-DEPENDENT PHYSICAL CHARACTERISTICS OF THE ROTATING NONLOCAL NANOBEAMS SUBJECT TO A VARYING HEAT SOURCE AND A DYNAMIC LOAD

In this article, the influence of thermal conductivity on the dynamics of a rotating nanobeam is established in the context of nonlocal thermoelasticity theory. To this end, the governing equations are derived using generalized heat conduction including phase lags on the basis of the Euler–Bernoulli beam theory. The thermal conductivity of the proposed model linearly changes with temperature and the considered nanobeam is excited with a variable harmonic heat source and exposed to a time-dependent load with exponential decay. The analytic solutions for bending moment, deflection and temperature of rotating nonlocal nanobeams are achieved by means of the Laplace transform procedure. A qualitative study is conducted to justify the soundness of the present analysis while the impact of nonlocal parameter and varying heat source are discussed in detail. It also shows the way in which the variations of physical properties due to temperature changes affect the static and dynamic behavior of rotating nanobeams. It is found that the physical fields strongly depend on the nonlocal parameter, the change of the thermal conductivity, rotation speed and the mechanical loads and, therefore, it is not possible to neglect their effects on the manufacturing process of precise/intelligent machines and devices.

Interactions in a nonlocal thermoelastic hollow sphere with voids due to harmonically varying heat sources

The present work is devoted to discuss the transient wave propagation in an isotropic homogenous thermoelastic spherical body with voids due to harmonically varying heat sources in the context of nonlocal thermoelasticity. The constitutive relations and the governing equations are resolved by applying harmonic variations in time and transformed into coupled ordinary differential equations. The outer and the inner surfaces of the sphere are kept stress-free and free from void concentration. A harmonically varying heat source is supplied on the inner surface along the radial direction and the outer surface is assumed to be isothermal. Numerical simulations are implemented to the analytical results with the support of MATLAB software tool. Numerically, generated data are presented graphically for the field variables of interest (temperature, stresses, cubical dilation, displacement and void volume fraction field) and at the end analysis of these results are given.

Thermodynamic modeling of a laser pulse heating in a rotating microelongated nonlocal thermoelastic solid due to G‐N theory

AbstractRotation of a linear and homogenous microelongated thermoelastic medium with a uniform angular velocity are discussed in the present paper. The studied problem was considered as a perfecting conducting medium which irradiated by a non‐gaussian laser beam. The nonlocal thermoelasticity theory was motivated to discuss the model with the energy dissipation in Green‐Naghdi type III. Fourier and Laplace transforms are used to obtain the solution of the problem and get the considered physical quantities. The comparisons were computed numerically and represented graphically with different cases. The obtained results are applicable in many fields as earthquake engineering, nuclear physics, and manufacturing. It is found that the obtained results are significant.